MIMO Interference Alignment Research Articles

Hybrid Deep Learning Approach for 6G MIMO Channel Estimation and Interference Alignment HetNet Environments

Hybrid Deep Learning Approach for 6G MIMO Channel Estimation and Interference Alignment HetNet Environments

Achievable Sum Rate and Degrees of Freedom of Opportunistic Interference Alignment in MIMO Interfering Broadcast Channels

In this paper, the sum rate of opportunistic interference alignment (OIA) is analyzed in multiple-input-multiple-output interfering broadcast channels. The alignment metric upon which users are scheduled is based on the chordal distance between certain interfering subspaces at each receiver, and the closed-form expressions for the rates of the scheduled users are derived. Furthermore, we show that for a system in which each user has $N$ receive antennas and the $j$ th base station transmits $d_{j}$ data streams, where $\sum _{j=1}^{I}d_{j}={N}+1$ and ${N}\ge 2$ , the rate for each user can be approximated by the mean of a Gumbel random variable. Further analysis reveals that if the number of users in cell $i$ scales as $\rho ^{\alpha }$ , where $\rho $ is the normalized transmit power and $\alpha \in [{0,1}]$ , then cell $i$ can achieve $\alpha d_{i}$ degrees of freedom. The simulation results confirm the validity of the theoretical analysis and the accuracy of the approximation. Thus, the sum rate analysis provided herein is an effective performance evaluation method for multi-cell OIA.

Homotopy Continuation for Spatial Interference Alignment in Arbitrary MIMO X Networks

In this paper, we propose an algorithm to design interference alignment (IA) precoding and decoding matrices for arbitrary MIMO X networks. The proposed algorithm is rooted in the homotopy continuation techniques commonly used to solve systems of nonlinear equations. Homotopy methods find the solution of a target system by smoothly deforming the solution of a start system which can be trivially solved. Unlike previously proposed IA algorithms, the homotopy continuation technique allows us to solve the IA problem for both unstructured (i.e., generic) and structured channels such as those that arise when time or frequency symbol extensions are jointly employed with the spatial dimension. To this end, we consider an extended system of bilinear equations that include the standard alignment equations to cancel the interference, and a new set of bilinear equations that preserve the desired dimensionality of the signal spaces at the intended receivers. We propose a simple method to obtain the start system by randomly choosing a set of precoders and decoders, and then finding a set of channels satisfying the system equations, which is a linear problem. Once the start system is available, standard prediction and correction techniques are applied to track the solution all the way to the target system. We analyze the convergence of the proposed algorithm and prove that, for many feasible systems and a sufficiently small continuation parameter, the algorithm converges with probability one to a perfect IA solution. The simulation results show that the proposed algorithm is able to consistently find solutions achieving the maximum number of degrees of freedom in a variety of MIMO X networks with or without symbol extensions. Further, the algorithm provides insights into the feasibility of IA in MIMO X networks for which theoretical results are scarce.

Physical Layer Security Based on Interference Alignment in K-User MIMO Y Wiretap Channels

This paper studies the secure degree of freedom (SDOF) of the multiway relay wiretap system $K$ -user MIMO Y wiretap channel, where each legitimate user equipped with $M$ antennas intends to convey independent signals via an intermediate relay with $N$ antennas. There exists an eavesdropper which is equipped with $N_{e}$ antennas close to the legitimate users. In order to eliminate the multiuser interference and keep the system security, interference alignment is mainly utilized in the proposed broadcast wiretap channel (BWC) and multi-access BWC (MBWC), and cooperative jamming is adopted as a supplementary approach in the MBWC model. The general feasibility conditions of the interference alignment are deduced as $M \ge K-1, 2M > N$ and $N \ge (({K(K-1)})/2)$ . In the BWC model, we have deduced the secure degrees of freedom (SDOF) as $K\min \{M,N\}-\min \{N_{e},K(K-1)/2\}$ , which is always a positive value. While in the MBWC model, the SDOF is given by $K\min \{M,N\}$ . Finally, since the relay transmits the synthesized signals of the legal signal and the jamming signal in the MBWC model, we propose a power allocation scheme to maximize the secrecy rate. Simulation results demonstrate that our proposed power allocation scheme can improve secrecy rate under various antenna configurations.

Energy Efficiency Optimization With Interference Alignment in Multi-Cell MIMO Interfering Broadcast Channels

Characterizing the fundamental energy efficiency (EE) performance of multiple-input–multiple-output interfering broadcast channels (MIMO-IFBC) is important for the design of green wireless system. In this paper, we propose a new network architecture proposition based on EE maximization for Multi-Cell MIMO-IFBC within the context of interference alignment (IA). Particularly, EE is maximized subject to maximum power and minimum throughput constraints. We propose two schemes to optimize EE for different signal-to-noise ratio (SNR) regions. For high-SNR operating regions, we employ a grouping-based IA scheme to jointly cancel intra- and inter-cell interferences and thus transform the MIMO-IFBC to a single-cell MIMO scenario. A gradient-based power adaptation scheme is proposed based on water-filling power adaptation and singular value decomposition to maximize EE for each cell. For moderate SNR cases, we propose an approach using dirty paper coding (DPC) with the principle of multiple access channel and broadcast channel duality to perform IA while maximizing EE in each cell. The algorithm in its dual form is solved using a subgradient method and a bisection searching scheme. Simulation results demonstrate the superior performance of the proposed schemes over several existing approaches. It also shows that interference-nulling-based IA approaches outperform hybrid DPC-IA approach in high-SNR region, and the opposite occurs in low-SNR region.

Antenna Configurations for MIMO Interference Alignment in Three-User Heterogeneous Systems

Recently, heterogeneous network (HetNet) has been introduced as an appropriate strategy to cope with the explosive growth of wireless traffic. To address the issue of severe interference in the HetNet, we can consider interference alignment (IA), which achieves the maximum degrees of freedom (DOFs) in multiple-input-multiple-output (MIMO) interference channels (ICs). However, an anticipated performance of the MIMO IA is difficult to be clarified, particularly with different numbers of antennas across the nodes when designing an appropriate system. In this paper, we thus study antenna configurations for the three-user MIMO IA with respect to the intended data stream tuple, i.e, DOF. For simple analysis, we consider two-tier network with two types of data stream numbers in a system. First, the dimension of the subspace occupied by interference is derived by aligning the interference in the signal space of the MIMO IA. After this, the suitable numbers of antennas are computed depending on the transmitted data stream numbers. Our obtained results provide an insight on how the performance of the MIMO IA is affected as the system configurations change. Furthermore, we discuss how to maximize the performance of such systems when the available numbers of antennas are finite. The actual simulations with an iterative IA confirm the validity of our derived results.

Interference Alignment with Limited Feedback Based on Double Codebook

While Interference Alignment (IA) based on direct method needs perfect channel state information, this is difficult to achieve in real communication system. In the MIMO interference alignment system with limited feedback based on only one codebook, the channel coefficient matrices are quantified at receivers, then the precoding matrix can be designed with the quantified channel coefficient matrices got in the feedback scheme at transmitters, finally interference alignment can be achieved when perfect channel state information is not available. But if better sum rate performance is wanted, the size of the codebook used to quantify the channel coefficient matrices and the calculation of the quantization will increase much more. In order to reduce the size and complexity of the codebook, we proposed a new channel quantization method to optimize the performance of IA with limited feedback. In our proposed scheme, we use a linear combination of two vectors to quantify the channel coefficient matrices instead of one vector. Simulation results show that the proposed scheme can achieve almost the same performance with smaller codebooks.

Iterative Transceiver Design for Opportunistic Interference Alignment in MIMO Interfering Multiple-Access Channels

In this paper, we propose an iterative transceiver design algorithm for opportunistic interference alignment in MIMO interfering multiple-access channels. The proposed algorithm iteratively optimizes the transmit beamforming vectors, the receive matrices and the user selection set, which digs into the multiuser diversity gain. Specifically, data transmission can be operated in each iteration using the updated transceiver and the selected user set, which means that no additional processing delay is introduced. Simulation results demonstrate the improved average rate per cell performance of the proposed algorithm compared to the conventional ones. Index Terms—Interference alignment, OIA, user scheduling, iterative

Transceiver Design Based on Interference Alignment in MIMO Interfering Broadcast Channels

In this paper, we develop a non-iterative transceiver design based on interference alignment (IA) for MIMO interfering broadcast channels with arbitrary number of cells and users per cell. By aligning the interference from other cells efficiently, we show that the proposed transceiver design can achieve the degrees of freedom (DOF) of d per user, i.e. total DOF of equation, where C is the number of cells, K i is the number of users for the i-th cell, and d is the number of streams per user. We also investigate conditions for the antenna configuration in order to attain the total DOF of equation. From simulation results, we demonstrate that the proposed transceiver design can obtain higher DOF than the conventional scheme under equal antenna configuration.

User Arrival in MIMO Interference Alignment Networks

In this paper we analyze a constant multiple-input multiple-output interference channel where a set of active users are cooperating through interference alignment while a set of secondary users desire access to the channel. We find the minimum number of secondary transmit antennas required so that a secondary user can use the channel without affecting the sum rate of the active users, under a zero-forcing equalization assumption. When the secondary users have enough antennas, we derive several secondary user precoders that approximately maximize the secondary users' sum rate without changing the sum rate of the active users. When the secondary users do not have enough antennas, we perform numerical optimization to find secondary user precoders that cause minimum degradation to the sum rate of the active users. Through simulations, we confirm that i) with enough antennas at the secondary users, gains equivalent to the case of all the users cooperating through interference alignment is obtainable, and ii) when the secondary users do not have enough antennas, large rate losses at the active users can be avoided.channels

MIMO Interference Alignment Over Correlated Channels With Imperfect CSI

Interference alignment (IA), given uncorrelated channel components and perfect channel state information, obtains the maximum degrees of freedom in an interference channel. Little is known, however, about how the sum rate of IA behaves at finite transmit power, with imperfect channel state information, or antenna correlation. This paper provides an approximate closed-form signal-to-interference-plus-noise-ratio (SINR) expression for IA over multiple-input-multiple-output (MIMO) channels with imperfect channel state information and transmit antenna correlation. Assuming linear processing at the transmitters and zero-forcing receivers, random matrix theory tools are utilized to derive an approximation for the post-processing SINR distribution of each stream for each user. Perfect channel knowledge and i.i.d. channel coefficients constitute special cases. This SINR distribution not only allows easy calculation of useful performance metrics like sum rate and symbol error rate, but also permits a realistic comparison of IA with other transmission techniques. More specifically, IA is compared with spatial multiplexing and beamforming and it is shown that IA may not be optimal for some performance criteria.